# Toward Data-Driven Surrogates of the Solar Wind with Spherical Fourier Neural Operator

arXiv: https://arxiv.org/abs/2511.22112 · HTML: https://mlsanity.com/paper/2511.22112/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 23 references that are in the map.
- First posted on arXiv 27 Nov 2025.

## Builds on (most cited first, 6 of 6)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [Operator Learning: Algorithms and Analysis](https://mlsanity.com/paper/2402.15715/) (2024)
- [A Library for Learning Neural Operators](https://mlsanity.com/paper/2412.10354/) (2024)

## Built on by (most cited first, 3 of 3)

- [Deterministic and probabilistic neural surrogates of global hybrid-Vlasov simulations](https://mlsanity.com/paper/2601.12614/) (2026)
- [Neural Operator based Multi-Field Reconstruction of Inner Solar Boundary State](https://mlsanity.com/paper/2608.22782/) (2026)
- [A library for differentiable signal processing and machine learning on the sphere](https://mlsanity.com/paper/2609.39737/) (2026)

## Abstract (arXiv)

The solar wind, a continuous stream of charged particles from the Sun's corona, shapes the heliosphere and impacts space systems near Earth. Variations such as high-speed streams and coronal mass ejections can disrupt satellites, power grids, and communications, making accurate modeling essential for space weather forecasting. While 3D magnetohydrodynamic (MHD) models are used to simulate and investigate these variations in the solar wind, they tend to be computationally expensive, limiting their usefulness in investigating the impacts of boundary condition uncertainty. In this work, we develop a surrogate for steady state solar wind modeling, using a Spherical Fourier Neural Operator (SFNO). We compare our model to a previously developed numerical surrogate for this task called HUX, and we show that the SFNO achieves comparable or better performance across several metrics. Though HUX retains advantages in physical smoothness, this underscores the need for improved evaluation criteria rather than a flaw in SFNO. As a flexible and trainable approach, SFNO enables efficient real-time forecasting and can improve with more data. The source code and more visual results are available at https://github.com/rezmansouri/solarwind-sfno-velocity.